Problem: The sum of two numbers is $38$, and their difference is $10$. What are the two numbers?
Solution: Let $x$ be the first number, and let $y$ be the second number. The system of equations is: ${x+y = 38}$ ${x-y = 10}$ Solve for $x$ and $y$ using elimination. Add the top and bottom equations together. $ 2x = 48 $ $ x = \dfrac{48}{2} $ ${x = 24}$ Now that you know ${x = 24}$ , plug it back into $ {x+y = 38}$ to find $y$ ${(24)}{ + y = 38}$ ${y = 14}$ You can also plug ${x = 24}$ into $ {x-y = 10}$ and get the same answer for $y$ ${(24)}{ - y = 10}$ ${y = 14}$ Therefore, the larger number is $24$, and the smaller number is $14$.